{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7e2acac5",
   "metadata": {},
   "source": [
    "### Exact solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cab77013",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('Allen_Cahn.mat')\n",
    "\n",
    "# Following is the code to plot the data u vs x and t. u is 256*100\n",
    "# matrix. Use first 75 columns for training and 25 for testing :)\n",
    "\n",
    "# Access the variables stored in the .mat file\n",
    "# The variable names in the .mat file become keys in the loaded dictionary\n",
    "x = mat_data['x']\n",
    "t = mat_data['t']\n",
    "u = mat_data['u']\n",
    "\n",
    "# # Use the loaded variables as needed\n",
    "# print(x.shape)\n",
    "# print(t.shape)\n",
    "# print(u.shape)\n",
    "\n",
    "# X, T = np.meshgrid(x, t)\n",
    "# # Define custom color levels\n",
    "# c_levels = np.linspace(np.min(u), np.max(u), 100)\n",
    "\n",
    "# # Plot the contour\n",
    "# plt.figure()\n",
    "# plt.figure(figsize=(15, 5))\n",
    "# plt.contourf(T, X, u, levels=c_levels, cmap='coolwarm')\n",
    "# plt.xlabel('t')\n",
    "# plt.ylabel('x')\n",
    "# plt.title('Allen-cahn-Equation')\n",
    "# plt.colorbar()  # Add a colorbar for the contour levels\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84bf073b",
   "metadata": {},
   "source": [
    "### PINN data importing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1b028244",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20301, 2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the .mat file\n",
    "mat_data = scipy.io.loadmat('X.mat')\n",
    "\n",
    "X = mat_data['X']\n",
    "\n",
    "mat_data1 = scipy.io.loadmat('y_pred.mat')\n",
    "\n",
    "u1 = mat_data1['y_pred']\n",
    "\n",
    "np.set_printoptions(threshold=np.inf)\n",
    "\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "27f7472a",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Reshaping the solution\n",
    "\n",
    "u1 = u1.reshape(101, 201)\n",
    "u1_new = u1.T\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d177a69d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 101)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u1_new.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a82fd0d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tani (20301, 1)\n"
     ]
    }
   ],
   "source": [
    "# Load the .mat file\n",
    "mat_data2 = scipy.io.loadmat('y_true.mat')\n",
    "\n",
    "u2 = mat_data2['y_true']\n",
    "print(\"tani\", u2.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ed5635ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing libaries\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f74caeb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "class LEMCell(nn.Module):\n",
    "    def __init__(self, ninp, nhid, dt):\n",
    "        super(LEMCell, self).__init__()\n",
    "        self.ninp = ninp\n",
    "        self.nhid = nhid\n",
    "        self.dt = dt\n",
    "        self.inp2hid = nn.Linear(ninp, 4 * nhid)\n",
    "        self.hid2hid = nn.Linear(nhid, 3 * nhid)\n",
    "        self.transform_z = nn.Linear(nhid, nhid)\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        std = 1.0 / np.sqrt(self.nhid)\n",
    "        for w in self.parameters():\n",
    "            w.data.uniform_(-std, std)\n",
    "\n",
    "    def forward(self, x, y, z):\n",
    "        transformed_inp = self.inp2hid(x)\n",
    "        transformed_hid = self.hid2hid(y)\n",
    "        i_dt1, i_dt2, i_z, i_y = transformed_inp.chunk(4, 1)\n",
    "        h_dt1, h_dt2, h_y = transformed_hid.chunk(3, 1)\n",
    "\n",
    "        ms_dt_bar = self.dt * torch.sigmoid(i_dt1 + h_dt1)\n",
    "        ms_dt = self.dt * torch.sigmoid(i_dt2 + h_dt2)\n",
    "\n",
    "        z = (1. - ms_dt) * z + ms_dt * torch.tanh(i_y + h_y)\n",
    "        y = (1. - ms_dt_bar) * y + ms_dt_bar * torch.tanh(self.transform_z(z) + i_z)\n",
    "\n",
    "        return y, z\n",
    "\n",
    "# Define the LEM model\n",
    "class LEM(nn.Module):\n",
    "    def __init__(self, ninp, nhid, nout, dt=1.):\n",
    "        super(LEM, self).__init__()\n",
    "        self.nhid = nhid\n",
    "        self.cell = LEMCell(ninp, nhid, dt)\n",
    "        self.classifier = nn.Linear(nhid, nout)\n",
    "        self.init_weights()\n",
    "\n",
    "    def init_weights(self):\n",
    "        for name, param in self.named_parameters():\n",
    "            if 'classifier' in name and 'weight' in name:\n",
    "                nn.init.kaiming_normal_(param.data)\n",
    "\n",
    "    def forward(self, input):\n",
    "        y = input.data.new(input.size(1), self.nhid).zero_()\n",
    "        z = input.data.new(input.size(1), self.nhid).zero_()\n",
    "        for x in input:\n",
    "            y, z = self.cell(x, y, z)\n",
    "        out = self.classifier(y)\n",
    "        return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1c60d23c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Toy problem data\n",
    "input_size = 201  # number of columns in a dataset\n",
    "hidden_size = 32  # number of neurons\n",
    "output_size = 201\n",
    "sequence_length = 80  # number of sequences/ number of rows\n",
    "batch_size = 1\n",
    "num_epochs = 20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0b0d588d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# data = scipy.io.loadmat('y_pred.mat')\n",
    "u1 = u1_new\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9e2e9c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test data shape (201,)\n",
      "input data shape (201, 80)\n",
      "Target data shape (201, 80)\n"
     ]
    }
   ],
   "source": [
    "input_data = u1[:, 0:80]\n",
    "target_data = u1[:, 1:81]\n",
    "\n",
    "test_data = u1[:, 80] ### Change here\n",
    "#test_target = u1[:, 81:101]\n",
    "\n",
    "print(\"test data shape\", test_data.shape)\n",
    "#print(\"test target shape\", test_target.shape)\n",
    "\n",
    "print(\"input data shape\",input_data.shape)\n",
    "print(\"Target data shape\",target_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9c682113",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input tensor shape torch.Size([1, 80, 201])\n",
      "Target tensor shape torch.Size([1, 80, 201])\n"
     ]
    }
   ],
   "source": [
    "# Convert data to tensors\n",
    "input_tensor = torch.tensor(input_data.T).view(batch_size, sequence_length, input_size).float()\n",
    "target_tensor = torch.tensor(target_data.T).view(batch_size, sequence_length, output_size).float()\n",
    "\n",
    "print(\"input tensor shape\",input_tensor.shape)\n",
    "print(\"Target tensor shape\",target_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6910db13",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert test data to tensors\n",
    "test_tensor = torch.tensor(test_data.T).view(batch_size, 1, input_size).float()\n",
    "#test_target_tensor = torch.tensor(test_target.T).view(batch_size, 20, output_size).float()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1bbfd754",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/data/localhome/tkapoor/anaconda3/lib/python3.9/site-packages/torch/nn/modules/loss.py:530: UserWarning: Using a target size (torch.Size([1, 80, 201])) that is different to the input size (torch.Size([80, 201])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  return F.mse_loss(input, target, reduction=self.reduction)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10/20000, Loss: 0.0001731834636303\n",
      "Epoch: 20/20000, Loss: 0.0000321372244798\n",
      "Epoch: 30/20000, Loss: 0.0000150902060341\n",
      "Epoch: 40/20000, Loss: 0.0000054880197240\n",
      "Epoch: 50/20000, Loss: 0.0000040106374399\n",
      "Epoch: 60/20000, Loss: 0.0000035397408737\n",
      "Epoch: 70/20000, Loss: 0.0000034448728456\n",
      "Epoch: 80/20000, Loss: 0.0000034425800095\n",
      "Epoch: 90/20000, Loss: 0.0000034410566059\n",
      "Epoch: 100/20000, Loss: 0.0000034397110085\n",
      "Epoch: 110/20000, Loss: 0.0000034384645460\n",
      "Epoch: 120/20000, Loss: 0.0000034372890241\n",
      "Epoch: 130/20000, Loss: 0.0000034361623875\n",
      "Epoch: 140/20000, Loss: 0.0000034350900933\n",
      "Epoch: 150/20000, Loss: 0.0000034340637285\n",
      "Epoch: 160/20000, Loss: 0.0000034337635952\n",
      "Epoch: 170/20000, Loss: 0.0000034337635952\n",
      "Epoch: 180/20000, Loss: 0.0000034337635952\n",
      "Epoch: 190/20000, Loss: 0.0000034337635952\n",
      "Epoch: 200/20000, Loss: 0.0000034337635952\n",
      "Epoch: 210/20000, Loss: 0.0000034337635952\n",
      "Epoch: 220/20000, Loss: 0.0000034337635952\n",
      "Epoch: 230/20000, Loss: 0.0000034337635952\n",
      "Epoch: 240/20000, Loss: 0.0000034337635952\n",
      "Epoch: 250/20000, Loss: 0.0000034337635952\n",
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      "Epoch: 1500/20000, Loss: 0.0000034337635952\n",
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      "Epoch: 1540/20000, Loss: 0.0000034337635952\n",
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     ]
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 18710/20000, Loss: 0.0000034337635952\n",
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      "Epoch: 19930/20000, Loss: 0.0000034337635952\n",
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      "Epoch: 19970/20000, Loss: 0.0000034337635952\n",
      "Epoch: 19980/20000, Loss: 0.0000034337635952\n",
      "Epoch: 19990/20000, Loss: 0.0000034337635952\n",
      "Epoch: 20000/20000, Loss: 0.0000034337635952\n"
     ]
    }
   ],
   "source": [
    "# # dt=0.25, 0.15\n",
    "lem = LEM(input_size, hidden_size, output_size, dt=0.25)\n",
    "\n",
    "# Loss and optimizer\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.LBFGS(lem.parameters(), lr=0.1)\n",
    "\n",
    "# # Loss and optimizer\n",
    "# criterion = nn.MSELoss()\n",
    "# optimizer = torch.optim.Adam(lem.parameters(), lr=0.001)\n",
    "\n",
    "# Training loop\n",
    "for epoch in range(num_epochs):\n",
    "    def closure():\n",
    "        optimizer.zero_grad()\n",
    "        output = lem(input_tensor)\n",
    "        loss = criterion(output, target_tensor)\n",
    "        loss.backward()\n",
    "        return loss\n",
    "\n",
    "    optimizer.step(closure)\n",
    "\n",
    "    # Print progress\n",
    "    if (epoch + 1) % 10 == 0:\n",
    "        print(f'Epoch: {epoch + 1}/{num_epochs}, Loss: {closure().item():.16f}')\n",
    "\n",
    "    # Flatten prediction tensor\n",
    "    prediction = lem(input_tensor).view(-1).detach().numpy()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "78de0827",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 1, 201])\n",
      "torch.Size([1, 20, 201])\n"
     ]
    }
   ],
   "source": [
    "print(test_tensor.shape)\n",
    "prediction_tensor = torch.zeros(1, 20, 201).float()\n",
    "print(prediction_tensor.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "297a16fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 1, 201])\n",
      "(201, 1)\n",
      "(201, 1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    prediction = lem(test_tensor)\n",
    "    prediction = prediction.view(1, 1, 201).float()\n",
    "    prediction_tensor[:, 0, :] = prediction\n",
    "    for i in range(19):\n",
    "        prediction = lem(prediction)\n",
    "        prediction = prediction.view(1, 1, 201).float()\n",
    "        prediction_tensor[:, i+1, :] = prediction\n",
    "        \n",
    "print(prediction.shape)\n",
    "\n",
    "final_out = prediction.detach().numpy().reshape(-1,1)\n",
    "final_true = u[-1,:].reshape(-1,1)\n",
    "\n",
    "print(final_out.shape)\n",
    "print(final_true.shape)\n",
    "\n",
    "x = x.reshape(-1, 1)\n",
    "\n",
    "plt.plot(x, final_out)\n",
    "plt.plot(x, final_true)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4b7206d",
   "metadata": {},
   "source": [
    "### error at final time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f25db352",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test:  0.00475693257946669 \n"
     ]
    }
   ],
   "source": [
    "# Convert NumPy arrays to PyTorch tensors\n",
    "final_out_tensor = torch.from_numpy(final_out)\n",
    "final_true_tensor = torch.from_numpy(final_true)\n",
    "# final_true_tensor = torch.abs(final_true_tensor)\n",
    "\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean((final_out_tensor - final_true_tensor)**2)/torch.mean(final_true_tensor**2)\n",
    "print(\"Relative Error Test: \", relative_error_test.item(), \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dae20135",
   "metadata": {},
   "source": [
    "### Error in whole testing dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5eaf1fee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# exact\n",
    "u_test = u\n",
    "u_test_full = u_test[80:100, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "20d9252f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 201)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_test_full.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8d1fb210",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 20, 201])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_tensor.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e445eba",
   "metadata": {},
   "source": [
    "### L2 norm "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89d4bc2d",
   "metadata": {},
   "source": [
    "### Changed prediction tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ee9bf8bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "k1 = (prediction_tensor - u_test_full)**2\n",
    "u_test_full_tensor = torch.tensor(u_test_full**2)\n",
    "u_test_full_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7a13682f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test:  0.001357193380113211 %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean(k1)/ torch.mean(u_test_full_tensor)\n",
    "\n",
    "print(\"Relative Error Test: \", relative_error_test.item(), \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa356244",
   "metadata": {},
   "source": [
    "### Max absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d4df8fb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "R_abs = torch.max(prediction-u_test_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "765c1b67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.1604, dtype=torch.float64)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_abs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53123052",
   "metadata": {},
   "source": [
    "### mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "39b783e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "R_mean = torch.mean(torch.abs(prediction - u_test_full))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0e98bd87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.0297, dtype=torch.float64)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3e6557b",
   "metadata": {},
   "source": [
    "### Explained variance error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f147aa3c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Score: 0.9974217916181408\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "a = prediction\n",
    "b = u_test_full\n",
    "# Assuming 'a' is your predicted values (model's predictions) and 'b' is the true values (ground truth)\n",
    "# Make sure 'a' and 'b' are PyTorch tensors\n",
    "b = torch.tensor(b)\n",
    "# Calculate the mean of 'b'\n",
    "mean_b = torch.mean(b)\n",
    "\n",
    "# Calculate the Explained Variance Score\n",
    "numerator = torch.var(b - a)  # Variance of the differences between 'b' and 'a'\n",
    "denominator = torch.var(b)    # Variance of 'b'\n",
    "evs = 1 - numerator / denominator\n",
    "\n",
    "print(\"Explained Variance Score:\", evs.item())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a2555b6",
   "metadata": {},
   "source": [
    "### Contour plot 80 PINN and 20 LEM solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "088f6ee2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([20, 201])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_tensor = torch.squeeze(prediction_tensor)\n",
    "prediction_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "656a2d06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1, 201])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2cd25700",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 80, 201])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "37ac5ef9",
   "metadata": {},
   "outputs": [],
   "source": [
    "conc_u = torch.squeeze(input_tensor)\n",
    "prediction_tensor = torch.squeeze(prediction_tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "249d001b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([100, 201])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concatenated_tensor = torch.cat((conc_u, prediction_tensor), dim=0)\n",
    "\n",
    "concatenated_tensor.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "99f14a63",
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = np.linspace(0, 1 , 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b620cee4",
   "metadata": {},
   "source": [
    "#### Snapshots at particular time\n",
    "### t = 0.81, 0.99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "767a1e8a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b0f931ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "# # Make sure the font is Times Roman\n",
    "# plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "# # Perform the prediction\n",
    "# with torch.no_grad():\n",
    "#     prediction = lem(test_tensor)\n",
    "\n",
    "final_time_output = prediction_tensor[-2, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-2, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.99}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "\n",
    "# Increase font size for x and y axis numbers\n",
    "ax.tick_params(axis='both', which='major', labelsize=24)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('LEM_0.99_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3ac2cc78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "# Create the figure and axis objects with reduced width\n",
    "fig, ax = plt.subplots(figsize=(5, 5))  # You can adjust the width (7 inches) and height (5 inches) as needed\n",
    "\n",
    "# Make sure the font is Times Roman\n",
    "plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "# Perform the prediction\n",
    "with torch.no_grad():\n",
    "    prediction = lem(test_tensor)\n",
    "\n",
    "final_time_output = prediction_tensor[-20, :]\n",
    "final_out = final_time_output.detach().numpy().reshape(-1, 1)\n",
    "final_true = u[-20, :].reshape(-1, 1)\n",
    "\n",
    "# Plot the data with red and blue lines, one with dotted and one with solid style\n",
    "ax.plot(x, final_out, color='red', linestyle='dotted', linewidth=12, label='Prediction')\n",
    "ax.plot(x, final_true, color='blue', linestyle='solid', linewidth=7, label='True')\n",
    "\n",
    "# Set the axis labels with bold font weight\n",
    "ax.set_xlabel(r\"${x}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "ax.set_ylabel(r\"${u(x, t)}$\", fontsize=26, color='black', fontdict={'weight': 'bold'})\n",
    "\n",
    "# Set the title with bold font weight\n",
    "ax.set_title(r\"${t = 0.81}$\", fontsize=26, color='black', fontweight='bold')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 3\n",
    "ax.set_xticks([-1, 0, 1])\n",
    "ax.set_yticks([-1, 0, 1])\n",
    "\n",
    "# Set tick labels fontweight to bold and increase font size\n",
    "ax.tick_params(axis='both', which='major', labelsize=20, width=2, length=10)\n",
    "\n",
    "# # Set the fontweight for tick labels to bold\n",
    "# for tick in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "#     tick.set_weight('bold')\n",
    "\n",
    "# Set the spines linewidth to bold\n",
    "ax.spines['top'].set_linewidth(2)\n",
    "ax.spines['right'].set_linewidth(2)\n",
    "ax.spines['bottom'].set_linewidth(2)\n",
    "ax.spines['left'].set_linewidth(2)\n",
    "\n",
    "# Set the legend\n",
    "# ax.legend()\n",
    "\n",
    "plt.savefig('LEM_0.81_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acd9f6c3",
   "metadata": {},
   "source": [
    "### 80-20 (80 for PINN and 20 extrapolation using LEM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "11b46593",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "findfont: Font family ['Times New Roman'] not found. Falling back to DejaVu Sans.\n",
      "findfont: Font family ['Times New Roman'] not found. Falling back to DejaVu Sans.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FixedLocator\n",
    "\n",
    "# Assuming you have defined concatenated_tensor as a PyTorch tensor\n",
    "# concatenated_tensor = torch.cat((tensor1, tensor2), dim=0)\n",
    "\n",
    "# Convert concatenated_tensor to a NumPy array\n",
    "concatenated_array = concatenated_tensor.numpy()\n",
    "\n",
    "# Define custom color levels\n",
    "x = np.linspace(0, 1, concatenated_array.shape[1])  # Replace 0 and 1 with your actual x range\n",
    "t = np.linspace(0, 1, concatenated_array.shape[0])  # Replace 0 and 1 with your actual t range\n",
    "X, T = np.meshgrid(x, t1)\n",
    "\n",
    "# Define custom color levels using the minimum and maximum from the NumPy array\n",
    "c_levels = np.linspace(np.min(concatenated_array), np.max(concatenated_array), 400)\n",
    "\n",
    "# Plot the contour with interpolated data\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.pcolormesh(T, X, concatenated_array, shading='auto', cmap='coolwarm')\n",
    "\n",
    "# Set the fontweight for axis labels to regular (not bold)\n",
    "plt.xlabel(\"$t$\", fontsize=26)\n",
    "plt.ylabel(\"$x$\", fontsize=26)\n",
    "plt.title(\"$u(x, t)$\", fontsize=26)\n",
    "\n",
    "# Set tick labels fontweight to regular (not bold) and increase font size\n",
    "plt.tick_params(axis='both', which='major', labelsize=20, width=3, length=10)\n",
    "\n",
    "# Set the fontweight for tick labels to regular (not bold)\n",
    "for tick in plt.gca().get_xticklabels() + plt.gca().get_yticklabels():\n",
    "    tick.set_weight('normal')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 5\n",
    "num_ticks = 5\n",
    "x_ticks = np.linspace(np.min(T), np.max(T), num_ticks)\n",
    "y_ticks = np.linspace(np.min(X), np.max(X), num_ticks)\n",
    "\n",
    "plt.gca().xaxis.set_major_locator(FixedLocator(x_ticks))\n",
    "plt.gca().yaxis.set_major_locator(FixedLocator(y_ticks))\n",
    "\n",
    "cbar1 = plt.colorbar()\n",
    "# Set the number of ticks for the color bar with uniformly distributed numbers\n",
    "num_ticks = 5\n",
    "c_ticks = np.linspace(np.min(concatenated_array), np.max(concatenated_array), num_ticks)\n",
    "cbar1.set_ticks(c_ticks)\n",
    "\n",
    "# Set the fontweight and fontsize for color bar tick labels\n",
    "for t in cbar1.ax.get_yticklabels():\n",
    "    t.set_weight('normal')\n",
    "    t.set_fontsize(26)  # Increase the font size for color bar tick labels\n",
    "\n",
    "# Increase the size of numbers on axis and color bar\n",
    "plt.xticks(fontsize=26)\n",
    "plt.yticks(fontsize=26)\n",
    "\n",
    "# Increase the tick size and width of the color bar\n",
    "cbar1.ax.tick_params(axis='both', which='major', labelsize=30, width=3,  length=10)\n",
    "\n",
    "# Add a dotted line at t = 0.8\n",
    "plt.axvline(x=0.8, color='black', linestyle='dotted', linewidth=5)\n",
    "\n",
    "#plt.savefig('Contour_LEM_20.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "plt.savefig('contour_LEM_20.jpeg', dpi=500, bbox_inches=\"tight\")\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e98c486",
   "metadata": {},
   "source": [
    "### exact solution contour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "40d9dede",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import FixedLocator\n",
    "\n",
    "# Assuming you have defined concatenated_tensor as a PyTorch tensor\n",
    "# concatenated_tensor = torch.cat((tensor1, tensor2), dim=0)\n",
    "\n",
    "# Convert concatenated_tensor to a NumPy array\n",
    "concatenated_array = u\n",
    "\n",
    "# Define custom color levels\n",
    "x = np.linspace(0, 1, concatenated_array.shape[1])  # Replace 0 and 1 with your actual x range\n",
    "t = np.linspace(0, 1, concatenated_array.shape[0])  # Replace 0 and 1 with your actual t range\n",
    "X, T = np.meshgrid(x, t)\n",
    "\n",
    "# Define custom color levels using the minimum and maximum from the NumPy array\n",
    "c_levels = np.linspace(np.min(concatenated_array), np.max(concatenated_array), 400)\n",
    "\n",
    "# Plot the contour with interpolated data\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.pcolormesh(T, X, concatenated_array, shading='auto', cmap='coolwarm')\n",
    "\n",
    "# Set the fontweight for axis labels to regular (not bold)\n",
    "plt.xlabel(\"$t$\", fontsize=26)\n",
    "plt.ylabel(\"$x$\", fontsize=26)\n",
    "plt.title(\"$u(x, t)$\", fontsize=26)\n",
    "\n",
    "# Set tick labels fontweight to regular (not bold) and increase font size\n",
    "plt.tick_params(axis='both', which='major', labelsize=20, width=3, length=10)\n",
    "\n",
    "# Set the fontweight for tick labels to regular (not bold)\n",
    "for tick in plt.gca().get_xticklabels() + plt.gca().get_yticklabels():\n",
    "    tick.set_weight('normal')\n",
    "\n",
    "# Set the number of ticks for x-axis and y-axis to 5\n",
    "num_ticks = 5\n",
    "x_ticks = np.linspace(np.min(T), np.max(T), num_ticks)\n",
    "y_ticks = np.linspace(np.min(X), np.max(X), num_ticks)\n",
    "\n",
    "plt.gca().xaxis.set_major_locator(FixedLocator(x_ticks))\n",
    "plt.gca().yaxis.set_major_locator(FixedLocator(y_ticks))\n",
    "\n",
    "cbar1 = plt.colorbar()\n",
    "# Set the number of ticks for the color bar with uniformly distributed numbers\n",
    "num_ticks = 5\n",
    "c_ticks = np.linspace(np.min(concatenated_array), np.max(concatenated_array), num_ticks)\n",
    "cbar1.set_ticks(c_ticks)\n",
    "\n",
    "# Set the fontweight and fontsize for color bar tick labels\n",
    "for t in cbar1.ax.get_yticklabels():\n",
    "    t.set_weight('normal')\n",
    "    t.set_fontsize(26)  # Increase the font size for color bar tick labels\n",
    "\n",
    "# Increase the size of numbers on axis and color bar\n",
    "plt.xticks(fontsize=26)\n",
    "plt.yticks(fontsize=26)\n",
    "\n",
    "# Increase the tick size and width of the color bar\n",
    "cbar1.ax.tick_params(axis='both', which='major', labelsize=30, width=3,  length=10)\n",
    "\n",
    "#plt.savefig('Contour_Exact.pdf', dpi=500, bbox_inches=\"tight\")\n",
    "plt.savefig('contour_exact.jpeg', dpi=500, bbox_inches=\"tight\")\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6627cf46",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
